Finding the points of intersection of two ellipses

[Physt]

Does anyone know where I can find an algorithm for the points of intersection of two ellipses existing with arbitrary center points and rotations and having 0, 1, 2, 3 or 4 points of intersection?

 

[Norwegian]

If you have the equations of two conic sections, you can find the intersection points by finding the zeros of a 4th degree resultant (in one variable) as shown here following the paragraph starting with "For the intersections of two conics"

I havn't quality checked the linked page, but at least this method seems sound.